Question

Let X~U(5,21) , calculate the expected value for this uniform distribution.

Answer 1

The probability density function of X is f(x) = 1/(21-5) = 1/16.

The expected value of X is $E[X] = \int_5^{21}xf(x)dx = \int_5^{21}\frac{x}{16} dx =\frac{x^2}{32}|_5^{21} =(21^2-5^2)/32 = 13$

Answer. E[X]=13